If a 2 - 3 a + 1 = 0 , then find ( i ) a 2 + 1 a 2 ( i i ) a 3 + 1 a 3 .

Given a 2 - 3 a + 1 = 0 a 2 + 1 = 3 a a + 1 a = 3 . . . . . . ( i ) Squaring both sides of E q ( i ) , we get: ( a + 1 a ) 2 = 3 2 a 2 + 1 a 2 + 2 = 9 a 2 + 1 a 2 = 9 - 2 = 7 Cubing both sides of E q ( i ) , we get: ( a + 1 a ) 3 = 3 3 a 3 + 1 a 3 + 3 ( a + 1 a ) = 27 a 3 + 1 a 3 + 3 × 3 = 27 a 2 + 1 a 3 = 27 - 9 = 18

If x + 1 x 2 = 3 , find x 3 + 1 x 3 .

On cubing x + 1 x , we get: x + 1 x 3 = x 3 + 1 x 3 + 3 x + 1 x x + 1 x 2 × x + 1 x = x 3 + 1 x 3 + 3 x + 1 x 3 × x + 1 x = x 3 + 1 x 3 + 3 x + 1 x x 3 + 1 x 3 = 3 x + 1 x − 3 x + 1 x x 3 + 1 x 3 = 0 Hence, the required answer is 0 .

If x = 5 - 2 6 , find the value of x + 1 x .

Given x = 5 - 2 6 . . . . . . . . . . . ( i ) 1 x = 1 5 - 2 6 = 1 5 - 2 6 × 5 + 2 6 5 + 2 6 = 5 + 2 6 5 2 - ( 2 6 ) 2 = 5 + 2 6 25 - 24 = 5 + 2 6 1 1 x = 5 + 2 6 . . . . . . . . . ( i i ) on adding equation (i) and (ii) we get x + 1 x = 10 ( x + 1 x ) 2 = x + 1 x + 2 . x 1 x ( x + 1 x ) 2 = 12 x + 1 x = 2 3

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Understanding ICSE Mathematics Class 9>Algebra>Chapter 3 - Expansions>EXERCISE 3.2

M L Aggarwal Solutions for Exercise 2: EXERCISE 3.2

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 2: EXERCISE 3.2

Attempt the practice questions from Exercise 2: EXERCISE 3.2 with hints and solutions to strengthen your understanding. Understanding ICSE Mathematics Class 9 solutions are prepared by Experienced Embibe Experts.